This does not ensure a proper mixing of the SMC algorithm, as the number of tempering steps needed can be quite high — and a high number of steps would require a higher number of particles, which becomes quite heavy in terms of memory costs — leading to a genealogy degeneracy. This is a severe limitation to the use of our current version of the method, and this prevents us from estimating the marginal likelihood of the model. Depsite the particle degeneracy, we notice that the last particles do mix adequately. Our chosen solution is thus to start with an SMC run, and use the final step to initialize a Hastings-Metropolis-Rosenbluth-Teller algorithm [1]}, [2]}. We describe thoroughly in the supplementary the proposal kernel we used, the main difficulty lying in the handling of the latent variables.
